Answer
Image 1 is a broad view, image 2 is a close-up on the region around P,
where the tangent plane and the surface are indistinguishable.
Work Step by Step
Suppose $f$ has continuous partial derivatives.
An equation of the tangent plane to the surface $z=f(x, y)$ at the point $P(x_{0}, y_{0}, z_{0})$ is
$z-z_{0}=f_{x}(x_{0}, y_{0})(x-x_{0})+f_{y}(x_{0}, y_{0})(y-y_{0})$
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Using geogebra CAS, define
$a(x,y)=f_{x}(x,y),$
$b(x,y)=f_{y}(x,y)$
point P($1,1,3e^{0.1})$,
and use formula (2), given above to define the tangent plane.
Image 1 is a broad view, image 2 is a close-up on the region around P, where the tangent plane and the surface are indistinguishable.
